# B According to Maxwell, a gamma ray can be as energetic as a radio wave (given equal E amplitudes)?

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1. Apr 11, 2017

### Cozma Alex

According to the old thery of light the energy carried by by a wave is proportional to the amplitude of the electric field not to the frequency as planck proposed, so an eletromagnetic radiation in the gamma spectrum carry the same energy as a radio one if their amplitude is the same?
They only different in frequency and wave lenght that doesn't affect the energy

(According to the old theory, i know that energy is proportional to the frequency)

2. Apr 11, 2017

### Ibix

The energy per photon depends on the wavelength. But classical EM only models situations where there are lots and lots of photon, so you have another variable in the energy carried by a wave - the number of photons in the beam. An energetic radio pulse has more photons than an equally energetic gamma pulse, basically.

Incidentally, energy is related to intensity rather than amplitude, I think.

3. Apr 11, 2017

### nasu

The energy "carried by the wave" does not have a well defined meaning. It depends on how long the wave does this carrying and what is the wave's extension in space. The waves are compared usually in terms of intensity, which is energy carried in 1s through a cross section of 1m2 (in SI units).
In both classic and QED models you can have waves with different frequencies and same intensity. The fact that the energy per photon at low frequency is lower does not mean you cannot have high intensity. It just takes more photons.

4. Apr 11, 2017

### Cozma Alex

But the number of photons is related to the amplitude of the wave? Since the square of amplitude in related to the intensity, right?

So then a gamma "wave" and a radio wave having same energy have different amplitude

Last edited: Apr 11, 2017
5. Apr 11, 2017

### nasu

The number of photons is proportional to intensity.

6. Apr 12, 2017

### Ibix

The energy in a classical EM wave is proportional to the square of the amplitude. It's also proportional to the photon count (assuming it's monochromatic). So, as nasu says, the number of photons is proportional to the intensity, not the amplitude.
No. Energy is proportional to amplitude squared. So two pulses with the same intensity have the same amplitude. They may, however, contain different numbers of photons if they have different frequencies.

7. Apr 12, 2017

### tech99

For radio engineering purposes, I think Intensity may conveniently be expressed as Power Flux Density in W/sq metre.

8. Apr 12, 2017

### nasu

9. Apr 12, 2017

### Cozma Alex

I found this: https://www.quora.com/If-you-have-t...d-that-mean-would-the-photon-have-more-energy

Can you please explain me how two waves with same amplitude can have different number of photons?
You guys said the number of photons is propotional to the intensity, and intesity is proportional to the energy, but the energy is related to the ^2 of the amplitude, then logically the number of the photons is related to the amplitude^2 , where is this chain wrong?

10. Apr 12, 2017

### nasu

Who said is wrong? Amplitude squared is proportional to intensity which is proportional to number of photons.Note that "proportional" does not mean equal.

11. Apr 12, 2017

### Cozma Alex

Ok, thanks :)

However, getting back in time when they didn't know that light is quantised, we take a gamma ray, and a radio wave , both waves gamma and radio have same amplitude, are the energy of the two waves equal?
Supposing they carry for the same ammount of time, and in the same extension of space

12. Apr 12, 2017

### nasu

Do you think that the energy of the waves depends on the history of our knowledge?
And again, energy of a wave is not something well defined. What do you mean by it?

13. Apr 12, 2017

### Cozma Alex

I mean density of energy, 1/2 ε E^2

14. Apr 12, 2017

### nasu

If E is the same for both waves, what do you think, would they have the same energy density or not?

15. Apr 12, 2017

### Cozma Alex

Yes i guess, but if E is the same for both then they have also same number of photons...

16. Apr 12, 2017

### nasu

You forget again that proportional is not equal. The number of photons may be proportional to E^2 but it may depend on frequency too. So your conclusion does not follow.
Actually the relation between E and photons seems to be a little tricky in QED. A wave with a well defined value of E may not have a defined number of photons but rather be a superposition of states with different number of photons. Imagining photons as well defined "particles" is not very realistic.

17. Apr 12, 2017

### Cozma Alex

I didn't know that the nuber of photons can depend also on frequency, i thought that only energy depends on frequency, however i got it, now i understand, if E is defined then the number of photons is not

18. Apr 12, 2017

### nasu

If you are interested in seeing the "ugly" details of quantization of the EM field, here is an example
https://ocw.mit.edu/courses/nuclear...-fall-2012/lecture-notes/MIT22_51F12_Ch10.pdf
Right on top of page 100 they show that the expectation value of the electric field for a state with definite photon number is zero.

You may know of a somewhat similar case in quantum mechanics. For a state with definite value of momentum, the position is undefined.

19. Apr 12, 2017

### Cozma Alex

That makes sense to me :), if the position of the photons is defined then the wave nature vanish

20. Apr 12, 2017

### nasu

I believe that the photons don't even "have" a position operator. So talking about the position does not make sense for photons.
The relationship between position and momentum was just an example of a similar concept, but for particles like electrons or protons.